There are two different ways you can interpret the information given in a demand curve.

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What these notes hope to do is to do a quick review of supply, demand, and equilibrium, with an emphasis on a more quantifiable approach.

Demand Curve (Big Picture)

The whole point of a demand curve is to find the relationship between the price of a good and the quantity that consumers wish to purchase (the quantity demanded).

Why does it matter? First off, a solid understanding of supply and demand is generally necessary to have an economic understanding of the world around you. Second, and as important, if firms have knowledge of the demand curve facing their firm, they will have the ability to make more informed pricing and output decisions. These decisions that will directly affect the firm’s profitability. This will be particularly true of firms with pricing power (monopoly power). For even more background, read the textbook.

I am going to assume that you have some understanding of the 1st Law of Demand. The 1st Law of Demand states, “ceteris paribus (holding other relevant factors constant), as the price of a good falls, the quantity demand of that good increases.” Basically, it states that demand curves are downward sloping. Interpretations of the Demand Curve

There are two different ways you can interpret the information given in a demand curve.

Horizontal Interpretation of Demand Curve - this is the interpretation of the demand curve you are most likely familiar with. The idea here is to pick a price, then move (horizontally) over to the demand curve. For example, if the price of a Honda Accord is $22,000, the quantity demanded of Honda Accords might be 450,000. That is, if the price is $22,000, consumers will wish to purchase 450,000 cars. Likewise, if the price of a Honda Accord is $20,000, the quantity demanded might be 500,000.

See the graph below. The reason we call this the horizontal interpretation should be apparent.

Vertical Interpretation of Demand Curve – this will be less familiar, and will come in handy when discussing consumer surplus, and later when we discuss price discrimination and other pricing strategies. The idea here is to pick a quantity, then move (vertically) up to the demand curve. We sometimes call the result the “height of the demand curve”. See the picture below.

$20,000 $22,000 PACCORD

QACCORD 450,000 500,000

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For instance, if the height of the demand curve facing a specialized pizza store at Q = 20 is $17, this means that the most a consumer will be willing to pay for the 20th pizza is $17.1

Likewise, if the height of the demand curve at Q = 25 is $13, this means the most a consumer will be willing to pay for the 25th pizza is $13.2

As eluded to above and in the previous footnote, price discrimination is a strategy where firms will try to charge different customers different prices. If the firm can come up with a way to charge the first

consumer $17 and the other consumer $13, it will earn more revenue than if it charges a price of $17 (only the 1st consumer will purchase the pizza) or a price of $13 (both consumers purchase the good).

Of course, we could use either interpretation on a demand curve, depending in which type of problem we are interested. We could have asked what is the most a consumer will be willing to pay for the 450,000th or the 500,000th Honda Accord.3 Likewise, we could ask how many pizzas that consumers will wish to purchase at a price of $13 or $17.4 Which interpretation we choose does not change the underlying demand curve. As you progress, you will find it makes more sense to use one interpretation or the other depending on the problem we are dealing with.

1

This consumer would be willing to purchase the 20th pizza for any price less than $17, but will not pay any price higher than $17. We sometimes call the height of the demand curve the marginal benefit, marginal value, or marginal willingness to pay.

2

If you recall the difference between an individual consumer’s demand curve and the market demand curve, we are discussing the market demand curve in this case. We know that individual’s demand curves are downward sloping. Individually, you would be willing to pay more for the 20th pizza then you would for the 25th pizza. Are you still hungry? However, when we look at the market (overall) demand curve for a product, we have combined every person’s individual demand curve. The consumer who was willing to pay $17 for the 20th and the consumer who was willing to pay $13 for the 25th pizza are likely to be different people, a point we shall revisit when we discuss price discrimination.

3

Some consumer would be willing to pay $22,000 for the 450,000th Honda Accord and some other consumer would be willing to pay $20,000 for the 500,000th Honda Accord. In this case, I am very sure these are different consumers. Do you know anyone who owns 50,000 Honda Accords?

4

Hopefully not surprisingly, the answers here are 25 and 20, respectively. $13

$17 PPIZZA

QPIZZA 20 25

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Ceteris Paribus Conditions for Demand Curves

Thus far, we have glossed over the 1st Law of Demand and the ceteris paribus conditions for demand. Some more very deep background that you should have learned before...

If, we were interested in the important factors determining the number of cars sold, surely the price of cars would be important. This is exactly what we hope to capture with a demand curve. A demand curve illustrates how the quantity of cars consumers wish to purchase changes as the price of cars changes, holding other relevant factors constant.5

On the other hand, many other things (aside from the price of cars) affect the number of cars people wish to purchase. We call these other things “demand shifters” or “ceteris paribus conditions for demand”. In order to draw a demand curve (to isolate the relationship between the own price of a car and the quantity demanded of cars), we must hold the ceteris paribus conditions constant.

On the other hand, when one of these ceteris paribus conditions changes, we must shift the demand curve in the appropriate direction.

What are these “demand shifters” or ceteris paribus conditions for the demand for cars?

Just to name a few: Price of gasoline / insurance / tires, price of trucks / bicycles / public transportation, incomes of consumers, quality and characteristics of cars, expectations about future car prices, … More in the next section...

Mathematical Expressions of Demand Curves

The following section borrows heavily from Baye’s Chapter 2, and uses the notation therein. We can learn something from mathematicians. Here is what they would write:

)

,

(

P

M

H

f

Q

_xd

=

_x _y

What does it mean? It means the quantity demanded of good X (

Q

_xd) is a function of, or depends on, the price of good X (

P

_x) the price of related goods (

P

_y), the income level of consumers (

M

) and other stuff (

H

).

In fact, we can get even more specific about the form of the relationship. While it is not necessarily the case, we often model demand curves as being linear.6 If so, we can write out a very simple numerical expression of a demand curve. For example:

M

P

Q

_xd

=

100 −

1₂ _x

−

2

_y

+

6

5

If you recall from your previous economics classes, in this case, we would call the price of the car the “own price”. The own price is the price of the good for which we are drawing the demand curve. 6

A linear demand curve is one with a constant slope of the demand curve. Mathematically, this means the power (exponent) on the

P

_x term is (implicitly) 1. We will focus on linear demand curves in this class. As an example of a non-linear demand curve, consider

Q

_xd

=

100 −

₂1

P

_x2

−

2 P

_y

+

6 M

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We will call this a demand function. The demand function contains a whole slew of information. First off, suppose you were told to draw the demand curve for good X. You would pull out a piece of graph paper, label the vertical axis

P

_x, the horizontal axis

Q

_x, and then you would be stuck.7 In fact, you cannot draw the demand curve without knowing the values of

P

_y and

M

, which are the ceteris paribus conditions for demand.

Suppose you were told that

M

= 10 and

P

_y = 30. In that case, you could simplify the demand function to the point where you could draw it.8

M

P

Q

x y

d

x

100

2

6

1

−

+

−

=

)

10 (

6 )

30 (

2

100 −

1₂

−

+

=

x d x

P

Q

60

100 −

1₂

−

+

=

_x d x

P

Q

x d x

P

Q

=

₁₀₀

−

₂1

y = 30, we start with: x d

x

P

Q

=

₁₀₀

−

₂1

Now we just do the algebra. You can take whatever steps get you to the end. I will begin by adding

x

P

2 1

to both sides:

100

2 1

=

+

_x d x

P

Q

Then subtract

Q

xdfrom both sides: d

x

Q

P

=

100 −

2 1

And multiply both sides by 2:

7

Why not label it

Q

_xd? You could. Eventually, we will have the quantity of good X supplied, as well, so often we will just be lazy and label it

Q

x.

8

It is just a coincidence in this case that the last two terms in the demand function cancel out. This will not always be the case. See also below the examples for when

M

and

P

_y change.

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d x

x

Q

P

=

200 −

2

Why have I done this? First off, you will see in a second that it is now very easy to find a second point on our demand curve. In addition, this expression will come in handy when we find the marginal revenue curve for the firm.

Graphing the Demand Function

Recall from out demand function that

Q

_xd

=

₁₀₀

−

₂1

P

_x

. By plugging in

P

_x = 0 in the expression above, we find that

Q

_xd = 100. This is one point on our demand curve. In fact, this is the horizontal intercept of the demand curve.

We also solved for the inverse demand function, finding that

P

_x

=

200 −

2 Q

d_x. By plugging in

Q

_xd=0, we find that

P

_x=200. It turns out this is the vertical intercept of the demand curve.

Because we have a linear demand function, to draw the line, we need only find two points on the line, which we have just done. Put these two points on a graph, connect the dots, and we are finished. See below.

$200 PX

QX 100

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Shifting the Demand Curve

What if

M

increases from $10 to $20? What happens to the demand curve? From a mathematical perspective, we can just plug and chug. But we would also like to go back to the intuitions as well. First the math…

M

P

Q

_xd

=

100 −

1₂ _x

−

2

_y

+

6 )

20 (

6 )

30 (

2

100 −

1₂

−

+

=

x

d

x

P

Q

=

₁₀₀

−

1₂

P

_x

)

When we change the demand function, we will also get a new inverse demand function. Taking the same steps as before (but leaving out the explanation of these steps), we get:

x d

x

P

Q

=

₁₆₀

−

₂1

160

2 1

=

+

_x d x

P

Q

d x x

Q

P

=

160 −

2 1

d x

x

Q

P

=

320 −

2

Now, we draw the new demand curve. From the demand function, I see that setting

P

y = $30. What would happen to the demand curve

if M fell to $5?10

Start over at the original values. What would happen if the price of good Y fell to $20?11 Start over at the original values. What would happen if the price of good Y rose to $40?12 More on Ceteris Paribus Conditions

In our original demand shift, an increase in

M

from $10 to $20 results in an increase in the demand for the good. That is, an increase in income has lead to an increase in income. In fact, this tells us that good X is a normal good.

But we also want to hone your intuition. We can make predictions about what happens to the demand curve without knowing anything about the actual mathematics of the demand curve.

Now is the time for a review of our ceteris paribus conditions. Our focus will be on how changes in our ceteris paribus conditions shift the demand curve.

10

The demand curve decreases (shifts left). The new vertical intercept would be $140 and the new horizontal intercept would be 70.

11

The demand curve increases (shifts right). The new vertical intercept would be $240 and the new horizontal intercept would be 120.

12

The demand curve decreases (shifts left). The new vertical intercept would be $160 and the new $200

PX

QX 100

D0 $320

200 D1

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Generally speaking, the ceteris paribus conditions can be classified into a few major groups” 1. Price of Related Goods – Substitutes and Complements.

2. Income of Consumers – Normal or Inferior Goods 3. Expectations of Future Prices

4. Other Stuff

Prices of Related Goods

Complements are things that are used together. The classic example is peanut butter and jelly. In the car example, cars and gas and cars and insurance would be complements.

Substitutes are alternatives. The classic example is butter and margarine. In the car example, car and trucks and are substitutes and cars and public transportation would also be substitutes.

Substitutes

You tend to know them when you see them, but the definitions are as follows:

Goods A and B are called substitutes, if, when the price of good A changes, the quantity demanded (demand curve) for good B changes in the same direction.

Say we examine Coke and Pepsi, which are substitutes. If the price of Coke increases, the demand for Pepsi will increase. Why? Because people will substitute from drinking Coke (whose price has increased) to drinking Pepsi.

When the price of Coke rises, at each and every price of Pepsi (the horizontal interpretation of a demand curve), there will be a larger quantity demanded of Pepsi on the new demand curve than the original demand curve. The change in the price of coke has caused the demand curve for Pepsi to shift to the right (an increase in demand).

In the car example, if the price of trucks rise, the demand for cars will increase (shift right). If the price of public transportation falls, the demand for cars will decrease (shift left). Complements

Goods A and B are called complements, if, when the price of good A changes, the quantity demanded (demand curve) for good B changes in the opposite direction.

Consider ink cartridges and printers. If the price of ink cartridges increases, the demand for printers will shift to the left, or decrease. Why? People will realize the overall cost of printing will have increased, and thus will cut back on their printer purchases

In the car example, an increase in the price of gas will decrease the demand for cars. A decrease in the price of car insurance would increase the demand for cars. The Numerical Example

Recall our original expression of the demand function:

Had two ugly errors here

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M

P

Q

_xd

=

100 −

1₂ _x

−

2

_y

+

6

Believe it or not, that expression tells us if the goods X and Y are complements. How can you tell? For every $1 increase in the price of good Y, the quantity demanded of good X falls by 2 units. This means the price of good Y and the quantity demanded of good X are changing in the opposite direction. From this, we can conclude the goods are complements. In fact, it is the sign (not the magnitude) on the

P

_y term that tells us this. In this case, we have

−

2 P

_yin the expression (the sign is negative), indicating complements.

If for example, the demand function were instead

M

P

Q

d _x _y

x

100

2

3

6

1

+

−

=

then X and Y would be substitutes.13

Not convinced? Go back to the example where the

P

y decreased to $20. What happened to the demand

curve for cars? What happened to the demand curve when

P

_y increased to $40? Income

Normal Goods

Good A is called a normal good, if, when the incomes of consumers changes, the quantity demanded (demand curve) for good A changes in the same direction.

Examples of normal goods include Saints tickets, steak dinners, SUVs, almost everything else. An increase in the incomes of Saints fans will increase the demand for Saints Tickets (shift right). A decrease in the incomes of SUV consumers will decrease the demand for SUVs (shift left).

Inferior Goods

Good A is called an inferior good, if, when the incomes of consumers changes, the quantity demanded (demand curve) for good A changes in the opposite direction.

Examples of inferior Goods include Ramen Noodles, SPAM, Mad Dog 20/20, used underwear. An increase in the incomes of consumers will decrease the demand for Ramen Noodles (shift left). A decrease in the incomes of consumers will increase the demand for SPAM (shift right).

13

If you are wondering about the meaning of the magnitude of the coefficient on the

P

_y term, that is a good thing to wonder. The magnitude of the coefficient indicates how closely related the goods are. A large coefficient (in absolute value or further from zero) indicates the goods are closely related. If we considered the demand for Pepsi, substitutes for Pepsi that might be included are the price of Coke and the price of orange juice. But the demand for Pepsi will be more sensitive to the price of Coke than the price of orange juice. Thus, we would expect a larger coefficient on PCOKE then POJ, even though both would be positive. More when we get to elasticities.

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The Numerical Example

The logic is the same as above. A positive coefficient on the

M

(in this case we have

6 M

) in the demand function indicates that a one unit increase in income leads to a 6 unit increase in the quantity demanded of good X. This is consistent with a normal good.

A negative coefficient on the M term in the demand functions indicates inferior goods, as

M

and the demand curve for good X change in the opposite direction.14

Not convinced? See the example above about

M

increasing from $10 to $20 or the exercise decreasing from $10 to $5.

Expectations of Future Prices

Quite simple. When people expect prices to fall in the future, the (current) demand falls. People delay their purchases.

When people expect prices to rise in the future, the (current) demand rises. People try to act ahead of the price increases.

This becomes interesting for firms that regularly schedule sales. On the one hand, the sale itself would tend to increase purchases (while the sale occurs) according to the 1st Law of Demand. On the other hand, if people expect the sale, they may curtail their purchases in the period leading up to the sale. Automakers with their model year-end closeout? “Last-year's” fashions? The hardback version of a book before the paperback comes out? Microsoft Vista? Dollar movie theaters?

Everything Else

I do not mind writing notes, but I do not want to write forever! Many other things can shift a demand curve.

Consumer Surplus

The height of the demand curve tells us the maximum amount a consumer is willing to pay for a unit of the good. But very seldom does this consumer actually pay this amount. If there is a gap between the two, we call this gap consumer surplus.

Consumer Surplus = Amount consumer is willing to pay - the amount they had to pay

Can we find this are graphically? We can. From the vertical interpretation of a demand curve, we know that the height of a demand curve at some quantity tells us the maximum amount a consumer was willing to pay. If we compare this to the price on the graph, we have consumer surplus.

Let’s go back to the pizza example, only we will add in some additional information and assume the price of pizza is $11. We can calculate the consumer surplus enjoyed for each individual unit of pizza

consumed.

14

Again, the magnitude determines how sensitive consumption of that good is to changes in income. Consider Kraft Mac & Cheese and restaurant meals. I believe both Mac & Cheese and restaurant meals are normal goods, and thus both will have positive coefficients on

M

in their respective demand functions. I would also expect the coefficient on

M

in the demand function for Mac & Cheese to be close to zero, while the coefficient on

M

in the demand function for restaurant meals to be larger. When people win the lottery, they do not a bunch more Mac & Cheese than they used to, but people likely do buy a bunch more restaurant meals than they used to. More when we get to elasticities.

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For example, at Q = 15, the height of the demand curve is $21, while the price is $11, so consumer surplus is $10 ($21 - $11 = $9). The idea is this consumer is getting a “deal”. They would have paid $10 more than they had to. The larger the consumer surplus, the larger is the welfare (happiness) of consumers. At Q = 20, the demand curve tells us the consumer is willing to pay $17, while the price is only $11, leaving consumer surplus of $6.

It should be easy for you to calculate consumer surplus on the 25th pizza.15

Adding consumer surplus up for each individual unit of the goods gets very tedious. Fortunately there is a calculus trick.

In general, if you want to add up the total consumer surplus for consuming Q units (where Q can be any quantity), simply add up the entire area that is (1) under the demand curve, (2) above the price that consumers pay, and (3) out to the quantity Q. See the picture below.

This will come in very handy when we talk about price discrimination. As a firm, wouldn’t you want to try to charge everyone the maximum they are willing to pay?

15

Consumer surplus is $2, as the consumer is willing to pay (the height of the demand curve) $13, while $13

$17 PPIZZA

QPIZZA 20 25

Demand $11

15 $21

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P

Q Q

Demand P

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Supply Curve (Big Picture)

The whole point of a supply curve is to find the relationship between the price of a good and the quantity that firms wish to produce (the quantity supplied).

I am going to assume that you have some understanding of the 1st Law of Supply. The 1st Law of Supply states, “ceteris paribus (holding other relevant factors constant), as the price of a good rises, the quantity supplied of that good increases.” Basically, it states that supply curves are upward sloping.

Interpretations of the Supply Curve

There are two different ways you can interpret the information given in a supply curve.

Horizontal Interpretation of Supply Curve - this is the interpretation of the supply curve you are most likely familiar with. The idea here is to pick a price, then move (horizontally) over to the supply curve. For example, if the price of a car is $22,000, the quantity supplied of cars might be 450,000. That is, if the price is $22,000, firms will wish to produce 450,000 cars. Likewise, if the price of a car is $24,000, the quantity supplied might be 500,000.

See the graph below. The reason we call this the horizontal interpretation should be apparent.

Vertical Interpretation of Supply Curve – again, less familiar, and will be discussed in greater detail when it comes to cost curves. Just as the demand curve illustrated the highest price a consumer would be willing to pay, a supply curve illustrates the lowest price a firm would be willing to accept to produce the good. The idea here is still to pick a quantity then move (vertically) up to the supply curve. We sometimes call the result the “height of the supply curve”. See the picture below.

For instance, if the height of the supply curve facing a specialized pizza store at Q = 20 is $15, this means that the least a firm will be willing to accept to produce the 20th pizza is $15.1

1

This producer would be willing to produce the 20th pizza for any price above $15, but will not produce for any price less $15. The height of the supply curve is called the marginal cost of producing, a term we will

$24,000 $22,000

PCAR

QCAR 450,000 500,000

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Likewise, if the height of the supply curve at Q = 25 is $19, this means the least a firm would be willing to accept for the 25th pizza is $19.2

And as was case for demand, we can use either interpretation of a supply curve, depending in which type of problem we are interested. We could have asked what is the least a firm would have been willing to accept to produce the 450,000th or the 500,000th car.3 Likewise, we could ask how many pizzas that firms will wish to purchase at a price of $15 or $19.4

Which interpretation we choose does not change the underlying supply curve. As you progress, you will find it makes more sense to use one interpretation or the other depending on the problem we are dealing with.

Ceteris Paribus Conditions for Supply Curves

Thus far, we have glossed over the 1st Law of Supply and the ceteris paribus conditions for supply. Some more very deep background that you should have learned before...

If, we were interested in the important factors determining the number of cars produced, surely the price of cars would be important. This is exactly what we hope to capture with a supply curve. A supply curve illustrates how the quantity of cars that firms wish to produce changes as the price of cars changes, holding other relevant factors constant.5

2

If you recall the difference between an individual firm’s supply curve and the market supply curve, I want to be discussing the market supply curve in this case. We know that individual’s supply curves are upward sloping. When we look at the market (overall) supply curve for a product, we have combined every firm’s individual supply curve. It may or may not be the case that the firm that was willing to produce the 20th unit for $15 is the same firm that is willing to produce the 25th pizza. More later…

3

Some firm would be willing to produce the 450,000th car for $22,000 and some firm (could be the same firm or a different firm) would be willing to produce the 500,000th car for $24,000.

4

Hopefully not surprisingly, the answers here are 20 and 25, respectively. 5

If you recall from your previous economics classes, in this case, we would call the price of the car the “own price”. The own price is the price of the good for which we are drawing the supply curve.

$15 $19 PPIZZA

QPIZZA 20 25

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On the other hand, many other things (aside from the price of cars) affect the number of cars firms wish to produce. We call these other things “supply shifters” or “ceteris paribus conditions for supply”.

In order to draw a supply curve (to isolate the relationship between the own price of a car and the quantity supplied of cars), we must hold the ceteris paribus conditions constant.

On the other hand, when one of these ceteris paribus conditions changes, we must shift the supply curve in the appropriate direction.

What are these “supply shifters” or ceteris paribus conditions for the supply of cars?

Just to name a few: Price of steel / wages of workers, price of trucks, technology of producing, expectations about future car prices.

)

,

(

P

W

H

f

Q

_xs

=

_x _r

What does it mean? It means the quantity supplied of good X (

Q

_xs) is a function of, or depends on, the price of good X (

P

_x) the price of technologically related goods (

P

_r), the price of inputs (

W

) and other stuff (

H

).6

While it is not necessarily the case, we often model supply curves as being linear.7 If so, we can write out a very simple numerical expression of a demand curve. For example:

W

P

Q

_xs

=

70 +

₃1 _x

−

2

_r

−

70

2

5

3 3

1

−

+

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Suppose you were told that

W

= 8 and

P

_r = 5. You could simplify the supply function to the point where you could draw it.

W

P

Q

_xs

=

70 +

₃1 _x

−

2

_r

−

5 )

8 (

5 )

5 (

2

70 +

₃1

−

=

_x s x

P

Q

40

10

70 +

₃1

−

=

x s x

P

Q

x s x

P

Q

=

₂₀

+

1₃

₃1

20 +

=

.

By plugging in

P

_x = 0 in the expression above, we find that

Q

_xs = 20. This is one point on our supply curve. In fact, this is the horizontal intercept of the supply curve.

We also solved for the inverse supply function, finding that

P

_x

=

−

60 +

(17)

However, as you can see, this information still helps us out in drawing the picture. But as we hinted at above, only the portion of the supply curve in the positive quadrant (with positive price and positive

quantity) is going to be relevant. Se we’ll end up discarding that lower (dotted) portion of the supply curve.

Sometimes is helps to throw in one more point. You’ll see above, I’ve chosen Q = 100, at random, and stuck that on the graph as well. If we plug in Q = 100 to the inverse supply function, we see:

s x

x

Q

P

=

−

60 +

3 )

100 (

3

60 +

−

=

x

P

240 =

x

P

20 $240 PX

QX 100

Supply 20

PX

QX Supply

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Shifting the Supply Curve

What if

W

decreases from $8 to $4? What happens to the supply curve? First the math, then the intuition.

W

P

Q

x r

s

x

70

3

2

5

1

−

+

=

)

4 (

5 )

5 (

2

70 +

₃1

−

=

x s x

P

Q

20

10

70 +

₃1

−

=

x s x

P

Q

x s x

P

Q

=

₄₀

+

₃1

(compare this to

Q

_xs

=

₂₀

+

₃1

P

_x

3

s x

x

Q

P

=

−

120 +

3

Now, we draw the new supply curve. From the supply function, I see that setting

P

Again, any change in a ceteris paribus conditions shifts the supply curve. That is, a change in anything but the own price, causes a shift in the supply curve.

One more note: having discussed both demand curves and supply curves at this point, it is worth noting that most changes affect only the demand curve or the supply curve. There are separate lists of ceteris paribus conditions for demand and ceteris paribus conditions for supply. A change in wages will shift the supply curve, but not the demand curve. A change in the income of consumers will shift the demand curve, but not the supply curve.

However, every so often something comes about that shifts both the supply curve and the demand curve, but these are fairly rare.10

9

Why is this called an increase in the supply curve? From the horizontal interpretation of the supply curve, notice that at any (and every) price, there is a larger quantity supplied on the new supply curve than there is on the old supply curve.

10

An example might be the discovery of AIDS in the market for prostitution. This would affect both suppliers of prostitution services and the customers of prostitution services. Expectations about future prices will also affect both supply and demand.

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Some exercises, you ask?

Start with original supply curve and

W

= $8 and

P

r = $5. What would happen to the supply curve if

W

rose to $12?11

Start over at the original values. What would happen if the price of the related good (

P

r) fell to $2?

12

Start over at the original values. What would happen if the price of the related good (

P

_r) rose to $8?13 More on Ceteris Paribus Conditions

In our original supply shift, a decrease in

W

from $8 to $4 resulted in an increase in the supply for the good. That is, a decrease in an input price has led to an increase in supply.

But we also want to hone your intuition. We can make predictions about what happens to the supply curve without knowing anything about the actual mathematics of the supply curve.

Now is the time for a review of our ceteris paribus conditions. Our focus will be on how changes in our ceteris paribus conditions shift the supply curve.

11

The supply curve decreases (shifts left). The new vertical intercept would be

P

_x= $0 and the new horizontal intercept would also be

Q

_xs = 0 (the supply curve starts at the origin).

P

_x = $300 and

Q

_xs = 100 would be another point.

s = 100 would be another point.

20 $240 PX

QX 100

S0 S1

$180

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Generally speaking, the ceteris paribus conditions for Supply can be classified into a few major groups”

1. Input Prices

2. Prices of Technologically Related Goods (substitutes and complements in production) 3. Expectations of Future Prices

4. Other Stuff

Input Prices

With input prices, a mix of the vertical interpretation of the supply curve and the horizontal interpretation of the supply curve is necessary.

Consider, as we did above, a decrease in wages, one of the firm’s input prices. That is, consider a decrease in an input price. It stands to reason that a firm would now be willing to accept a lower price to produce the good. Why? We know a firm, broadly speaking, won’t produce a good unless it covers it costs. Because the cost of production is decreasing, the firm can accept a lower price (and still cover it costs). For example, if the height of the old supply curve at some quantity Q was $12, and now wages fall, the firm might accept $11 to produce the Qth unit of the good. More generally, because the height of the supply curve tells us the lowest price a firm will accept to produce a good, a decrease in an input price will cause the supply curve to shift down, vertically.14

See the picture below.

But as soon as we see this picture, we want to go back to the horizontal interpretation of supply curve. When we discuss increases in supply or decreases in supply, we want you think of these as changes as shifts to the right or left (not up or down). So if you were presented with the picture shown below (the same two supply curves), and you were forced to describe it using the horizontal interpretation of a supply curve, hopefully you would conclude there has been a shift to the right of the supply curve, which we call an increase in supply.

14

If you are comfortable interpreting supply curves as marginal cost curves, than all we are saying is the marginal cost of production is reduced at each level of output. The supply curve (marginal cost curve) shifts down vertically.

Supply Supply’ PX

QX Q

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At the end of the day, a decrease in an input price leads to a rightward shift of the supply curve (an increase in supply). An increase in an input price leads to a shift to the left of the supply curve (a decrease in supply).

Don’t believe me? Go back to the example above where we change the wage from $8 to $4. You’ll see we had a rightward shift of the supply curve. Finally, for an increase in an input price, do the exercise where I suggested an increase in the wage from $8 to $12.

More examples?

What happens to the supply curve for pizza if there is a decrease in the price of tomato sauce?15 What happens to the supply curve for cars if there is an increase in the price of steel?16

Prices of Technologically Related Goods Technological Complements

Technological complements are things that are produced together.

Let’s imagine for expositional purposes that every time a donut is produced, a donut hole is also produced. Another example would be that at a slaughterhouse, every time a cow is slaughtered, there is both beef and a hide produced. Any situation in which a “byproduct” is involved would be an example of technological complements.

The main idea is that production of the one good might be influenced by the price of the other, because the production of both goods is linked. A more formal definition:

Goods A and B are called technological complements, if when the price of good A increases, the quantity supplied of Good B changes in the same direction.

Examples:

If the price of donut holes increases, the firm will react by increasing the quantity supplied of donuts (increase in supply).

15

The supply curve increases (shifts right). 16

Supply Supply’ PX

QX Q

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If the price of beef decreases, a firm would decrease the quantity of hides it will produce (decrease in supply).

Technological Substitutes

Technological substitutes are alternative products. General motors can use its equipment to produce compact cars or SUVs. A donut shop could produce crème filled donuts or danishes.

Goods A and B are called technological substitutes, if when the price of good A increases, the quantity supplied of Good B changes in the opposite direction.

Examples:

If the price of SUVs decreases, General Motors will increase the quantity supplied of compact cars (increase in supply). The logic here is that because the equipment is capable of producing both, producing SUVs will be less relatively less lucrative, and thus the firm will switch to producing compact cars. Sound familiar?

If the price of danishes increases, a donut shop will decrease its quantity supplied of donuts (decrease in supply). Now producing danishes will be more lucrative, so the firm will substitute from producing donuts to danishes.

The Numerical Example

Recall our original expression of the supply function:

W

P

Q

_xs

=

70 +

₃1 _x

−

2

_r

−

5

Recall that

P

_r indicates the price of the related good. Are goods X and the related good technological substitutes or technological complements?

_rterm would indicate technological complements.

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When firms expect prices to rise in the future, the current supply decreases. Firms will hold back production.

One detail here…take for example the second situation in which firms expect prices to rise in the future. While we say that current supply will decrease, we could be a bit more precise. What is likely to happen is that firms will continue to produce goods, but will not sell as many of these goods today, instead choosing to accumulate inventories, which they then expect to liquidate when prices rise in the future. In this regard, when we say supply, we are talking about those products that are brought to market, not the quantity of goods that are manufactured.18

You may also have noticed that if firms hold back production today in anticipation of future prices, this act itself may cause prices to increase now. More later…

Everything Else

I liked writing notes more last week… Many other things can shift a supply curve. Producer Surplus

My hope is that you can anticipate everything that is forthcoming here.

The height of the supply curve tells us the minimum amount a producer is willing to accept to produce a unit of the good. But seldom does this producer actually get paid this amount. If there is a gap between the two, we call this gap producer surplus.

Producer Surplus = Amount producer actually is paid - the minimum amount they would have accepted From the vertical interpretation of a supply curve, we know that the height of a supply curve at some quantity tells us the minimum amount a producer was willing to accept. If we compare this to the price on the graph, we have producer surplus.

Let’s go back to the pizza example, and assume the price of pizza is $22.

At Q = 15, the height of the supply curve is $11, while the price is $22, so consumer surplus is $11 ($22 - $11 = $11). The idea is that the producer is getting a deal. They would have accepted $11 for the good, but they received $22. If this $11 sounds something like profit, you’re on the right track.19

At Q = 20, producer surplus is $22 - $15 = $7.

It should be easy for you to calculate producer surplus on the 25th pizza.20

18

Not all firms have this option. For example, Domino’s pizza can not produce pizzas in August, and sell them in September.

19

If you are comfortable with interpreting supply curves as a marginal cost curve, producer surplus is the difference between P and marginal costs, sometimes called operating profit.

20

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Just as before, adding producer surplus up for each individual unit of the goods gets very tedious. We’ll use the same calculus trick.

In general, if you want to add up the total producer surplus for producing Q units (where Q can be any quantity), simply add up the entire area that is (1) above the supply curve, (2) below the price that suppliers receive, and (3) out to the quantity Q. See the picture below.

$15 $19 PPIZZA

QPIZZA 20 25

Supply

$11

15 $22

P

Q Q

Supply P

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Markets and Equilibrium

Market – a process or location in which equilibrium is established and the otherwise inconsistent aspirations of demanders and suppliers are reconciled.

Equilibrium - an outcome or state that will tend to persist unless disturbed by a change in one or more of the ceteris paribus conditions.

Is the equilibrium price PH?

I bet you guys know the drill, but as long as we’ve wandered down this path, we may as well wander a bit more. Let’s combine a supply curve (firm behavior) with a demand curve (consumer behavior) and see if we can’t see how things play out. Basically, what is the equilibrium price and quantity we will observe? Let’s try out PH. At this price, we find out how much suppliers want to produce by looking at their supply curve (QS1), and how much demanders want to consume by looking at the demand curve (QD1). At this price, QS1 > QD1. This is called an excess quantity supplied or surplus. Suppliers would like to supply more than demanders want to purchase (suppliers and demanders aspirations are not consistent). Suppliers will not be able to sell all that they wish to at this high price.

The surplus will cause downward pressure on price. As price falls, two things happen simultaneously. Suppliers desire to produce less as price lowers, and demanders desire to purchase more as price lowers. This causes the size of the surplus to decrease. The downward pressure on price will continue until the equilibrium price is reached and there is no longer a surplus.

Supply PH

PL

Demand

QD1 QS2 QD2 QS1 Quantity Is the equilibrium price PL?

Let’s try PL. At this price, we again find out how much suppliers want to produce by looking at their supply curve (QS2), and how much demanders want to consume by looking at the demand curve (QD2). At this price, QD2 > QS2. This is called an excess quantity demanded or shortage. At this low price, many consumers want to purchase the product, but suppliers will not be willing to produce as much as consumers desire (the aspirations of suppliers and demanders are inconsistent).

This will cause upward pressure on price. As the price rises, two things simultaneously happen. Suppliers desire to produce more as price rises, and demanders desire to purchase less as price rises. These two factors cause the size of the shortage to decrease. This upward pressure on price will continue until the equilibrium price is reached and the shortage disappears entirely.

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The equilibrium price is P*

Let’s try P*. Refer to the picture below. At P*, demanders want to purchase Q* units. At P*, suppliers want to supply Q* units. Everyone who is willing to pay P* can buy all the goods they want. Everyone who is willing to supply goods at P* is supplying what they want. Everyone’s aspirations are consistent and everyone is happy. Let’s all hold hands and sing. No one wants to change their behavior, hence an equilibrium.

Price

Supply

P*

Demand

Q* Quantity

P* and Q* are the equilibrium price and equilibrium quantity. Equilibrium occurs where the supply curve intersects the demand curve. In other words, at the equilibrium price, quantity supplied equals quantity demanded. There is neither a shortage, nor a surplus - we say that the market clears. Even if we find the market price temporarily away from the equilibrium price, these pressures will cause the price to tend to return to equilibrium price. This is why we say equilibrium will “tend to persist” unless there is a change in a ceteris paribus condition.

Comparative Statics

Finding equilibrium prices and quantities are nice, but the most useful thing we’ll get out of supply and demand analysis will be what we call comparative statics. Basically, we change a ceteris paribus condition for some good then we see what impact this will have on the equilibrium price and quantity of that good.

You can think of comparative statics exercises as a four part process. As your get more comfortable, you’ll breeze through these without doing them step by step.

1. Start in initial equilibrium (draw an initial S & D curve to start) 2. Change one or more of the ceteris paribus conditions

3. Examine the impact on demand or supply (shift the appropriate curve) 4. Examine new equilibrium (compare)

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Examples of Comparative Statics

Suppose we are looking at the market for oranges. The initial equilibrium is (P0, Q0). There is an increase in income. Oranges are a normal good. This causes an increase in demand (demand curve to shift to the right). At the original price, P0, there is now an excess quantity demanded, putting upward pressure on the price. The new equilibrium will be (P1, Q1). Both equilibrium price and quantity will increase.

Price S

P1 P0

D D’

Q0 Q1 Quantity

Now, suppose unusually cold weather occurs in Florida, destroying some of the orange crop. This causes a reduction in the supply of oranges (supply curve shifts left). The initial equilibrium is (P0, QO). The new equilibrium is (P1, Q1). The equilibrium price will increase and the equilibrium quantity will decrease. Price S’ S

P1 P0

D

Q1 Q0 Quantity What if more than one curve shifts?

Suppose we are looking at the market for prostitution. Suddenly, AIDS is developed. What happens to the prostitution market? Again, the initial equilibrium is (P0, QO). AIDS decreases the demand for

prostitution, as well as decreases the supply of prostitution. The new equilibrium is (P1, Q1). You can think of AIDS as a sort of increase in the cost of producing “prostitution services”. Prostitutes will need to be paid a higher price to incur the risk of contracting AIDS.

PPROSTITUTION

S’ S

P0

D’ D

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As it is drawn, the price does not appear to have changed. However, the change in price is ambiguous. This can be seen two ways. First, take the two changes one at a time.

Change Effect on P Effect on Q Decrease in supply increases decreases Decrease in demand decreases decreases

Total ambiguous decreases

The other way this can be shown is to use supply and demand shifts of different magnitudes. Draw this with a large demand curve shift and a small supply curve shift. Check your answer. Now draw it again with a large supply curve shift and a small demand curve shift. Compare. You should see that in one case the price rises, while in the other case, the price falls.

In general, if you simultaneously change both a ceteris paribus condition for both supply and for demand, either the direction in the change of price or the direction of the change in quantity will be ambiguous.

What about the math?

If we had a demand function and a supply function, can we solve for the equilibrium price? The answer is yes. Hurray!

Here is how. We noted above that the equilibrium price was the price where quantity demanded is equal to quantity supplied. The nice thing is the demand function tells us what quantity demanded will be at various prices, while the supply function tells us what quantity supplied will be at various prices. By setting quantity demanded equal to quantity supplied and solving for the price, we can determine the equilibrium price. Once we do this, we can plug the equilibrium price back into the demand function (or the supply function) to determine the equilibrium quantity. Let’s do an example with our hopefully now familiar demand function and supply function.

Recall we started with:

M

P

Q

x y

d

x

100

2

6

1

−

+

−

=

then assumed that

M

= 10 and

P

_y = 30, which resulted in:

x d

x

P

Q

=

₁₀₀

−

₂1

On the supply side, we started with:

W

P

Q

_xs

=

70 +

₃1 _x

−

2

_r

−

5

then assumed that

W

= 8 and

P

_r = 5, which simplified to:

x s

x

P

Q

=

₂₀

+

₃1

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( )

x x x x x x x d x d x

P

Q

=

⇒

=

⇒

=

⇒

=

−

⇒

+

=

x

P

Q

( )

96

20

32

52

20

₃1

3

1

=

+

=

+

=

+

=

x

s

x

P

Q

Indeed, the quantity demand equals quantity supplied.

One last thing we can do is to check the graph. Visually, our answer looks reasonable.

$200 PX

QX 100

D 20 52 $96

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Elasticities – Why?

Why should we bother with elasticities?

As we learn a bit more economics, one of the things we would like to do is to try to be more specific. If you think back to your first microeconomics course, we were happy with you telling us simply in what direction the price and quantity will change. As we progress, we will still want to know in what direction the price and quantity will change, but in addition, we’d like to know how much the price and quantity will

change. Elasticities enable us to answer these questions. Is it a big change in price or a small one? Further, and perhaps more importantly, a firm’s pricing decisions will be directly influenced by the elasticity of demand for the product it is selling.

Elasticities – What are they?

All elasticities will be a measure of sensitivity. The (own) price elasticity of demand measures how sensitive quantity demand is to changes in (own) price. The (own) price elasticity of supply measures how sensitive quantity supplied is to changes in (own) price. The income elasticity of demand measures, you guessed it, how sensitive demand is to changes in income. The cross price elasticity of demand measure how sensitive quantity demanded is to a change in the price of a different good (a substitute or

complement).

The next step is to come up with a classification of what is “sensitive” and what is “insensitive”. Consider the example below:

Suppose a $1 increase in the price of gas leads to a 500 gallon decrease in gas sold. Now, suppose a $1 increase in the price of a BMW leads to a 500 fewer BMW cars to be sold. Which of these is a “big” quantity response? Even though both changes involve an increase of $1 and a reduction in quantity of 500, my feeling is that car change is extremely sensitive, while the gas is not so sensitive. The point here is that measuring changes is dollars and units sold might not be appropriate. $1 is a big deal for gas, but not for cars. Perhaps measuring the changes in percentages would give us a better idea? This is in fact how elasticities are measured.

In general, an elasticity is the percentage change in one variable resulting from a 1% increase in another. (Own) Price Elasticity of Demand

(Own) Price Elasticity of Demand is defined as the percentage change in quantity demanded of a good resulting from a 1% increase in its price.

x d x Px

Qx

P

Q

E

∆

=

%

,

You should read this as “the percentage change in quantity demanded of good X divided by the percentage change in price of good X”. The notation “∆” means “change in”.

Of course, because demand curves are downward sloping, the elasticity of demand will always be a negative number. An increase in price (positive denominator) will lead to a reduction in quantity demanded (negative numerator), giving us a negative value of

E

_Qx_,_Px. Likewise, a decrease in price (negative denominator) will lead to an increase in quantity demanded (positive numerator), and again result in a negative value of

E

Qx,Px. Since the elasticity of demand is always negative, people often strip off the negative sign and talk about the absolute value of elasticity. If someone ever tells you the elasticity of